A simple global model of plate dynamics and mantle convection

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Abstract
Cooling and thickening of lithospheric plates with age and subduction result in large‐scale horizontal density contrasts tending to drive plate motions and mantle flow. We quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions. First, two‐dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions. We are unable to obtain platelike behavior in viscous models with traction‐free boundary conditions. The piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes. If the lithosphere has a Newtonian viscous rheology, the net force on any plate is a strong function of the effective grid spacing used, leading to ambiguities in interpretation. Incorporating a rigid‐plastic lithosphere, which fails at a critical yield stress, into the otherwise viscous model removes these ambiguities. The model is extended to the actual three‐dimensional (spherical) plate geometry. The observed velocities of rigid‐plastic plates are matched to the solution of the viscous Stokes equation at the lithosphere‐asthenosphere boundary. Body forces from the seismically observed slabs, from the thickening of the lithosphere obtained from the actual lithospheric ages, and from the differences in structure between continents and oceans are included. Interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included. The driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three‐dimensional global return flow and resistance to deformation at converging boundaries; the rms residual torque is ∼30% of the driving torque. The density contrasts within the plates themselves can reasonably account for plate motions. Body forces from convection in the interior may provide only a small net force on the plates. At converging boundaries the lithosphere has a yield stress of ∼100 bars; drag at the base of the plates is ∼5 bars and resists plate motion. The net driving forces from subducting slabs and collisional resistance are localized and approximately balance. Driving forces from lithospheric thickening are distributed over the areas of the plates, as is viscous drag. The approximate balance of these two forces predicts plate velocities uncorrelated with plate area, as observed. The model represents a specific case of boundary layer convection; the dynamical results are consistent with either upper mantle or mantle‐wide convection.